How much space does a zero KB file/folder take up?

Maybe, but the very fact that a zero KB file's
existence is recorded must take up some space, no?

Yes, if I'm remembering correctly, there really isn't such thing as a zero K file. All files take up space in increments that depend on the size of the hard drive. I've forgotten the details, but basically every file will take up one unit (block?) on the hard drive. There's a limit to the number of files a hard drive can hold (which is pretty high these days), which is where the basic block size comes from in the first place.

As for folders, I'm sure there's some slight space taken up in the disk directory or something by each folder, but I think that's probably a trivial amount of space unless you're talking about an obscene number of folders. (And keep in mind that you've probably got at least 10,000 folders on your boot drive, as a rough estimate based on the 27,000 files contained in just my home folder.)

But back to computers, can zero KB files/folders be
safely deleted…

Whether it can be deleted safely has nothing to do with its size and everything to do with its purpose. If you don't know what it's for, don't delete it until you do know.

Thousands of years ago a file would take up an entire block on a hard drive. The drive could keep track of 65,500 blocks, so the larger the drive, the larger the block. So even a one k file could take over an entire 512k block. Even though the file was one k nothing else could live in that block.
http://docs.info.apple.com/article.html?artnum=8647

In these days of modern times that is no longer true. There are thousands of tiny files in thousands of folder in OS X. I can appreciate the desire to keep your hard drive tidy, but only you will appreciate your efforts. Your computer won't care!

The folder report Zero KB because the folder has no contents.

A folder (or directory) on a hard disk is only useful for relative referencing of files. It has nothing to do with a files location on disk. As such, it is more of a logical, rather than physical container. The space you save by deleting an empty folder is probably the 5 bytes (or however many charaters are in the folder's name) that will be deleted from the catalog file.